scholarly journals Describing phase transitions in field theory by self-similar approximants

2019 ◽  
Vol 204 ◽  
pp. 02003
Author(s):  
V.I. Yukalov ◽  
E.P. Yukalova
Keyword(s):  
Field Theory ◽  
Phase Transitions ◽  
Coupling Parameter ◽  
Asymptotic Series ◽  
Quantum Field ◽  
Lattice Data ◽  
Borel Summation ◽  
Self Similar ◽  
Similar Approximation ◽  
Good Agreement

Self-similar approximation theory is shown to be a powerful tool for describing phase transitions in quantum field theory. Self-similar approximants present the extrapolation of asymptotic series in powers of small variables to the arbitrary values of the latter, including the variables tending to infinity. The approach is illustrated by considering three problems: (i) The influence of the coupling parameter strength on the critical temperature of the O(N)-symmetric multicomponent field theory. (ii) The calculation of critical exponents for the phase transition in the O(N)-symmetric field theory. (iii) The evaluation of deconfinement temperature in quantum chromodynamics. The results are in good agreement with the available numerical calculations, such as Monte Carlo simulations, Padé-Borel summation, and lattice data.

scholarly journals Converting neutron stars into strange stars: Instanton model

2014 ◽  
Vol 23 (09) ◽  
pp. 1450078
Author(s):  
Victor Ts. Gurovich ◽  
Leonid G. Fel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Detonation Wave ◽  
Neutron Stars ◽  
Quark Matter ◽  
Quantum Fluctuation ◽  
The Self ◽  
Quantum Field ◽  
Spherical Detonation ◽  
Self Similar

We calculate the quasiclassical probability to emerge the quantum fluctuation which gives rise to the quark-matter drop with interface propagating as the self-similar spherical detonation wave (DN) in the ambient nuclear matter. For this purpose, we make use of instanton method which is known in the quantum field theory.

Understanding Phase Transitions in Supersymmetric Quantum Electrodynamics With Resurgence Theory

2021 ◽  
Vol 1 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Transitions ◽  
Series Expansion ◽  
Quantum Electrodynamics ◽  
Quantum Field ◽  
Perturbative Series

Using resurgence theory to describe phase transitions in quantum field theory shows that information on non-perturbative effects like phase transitions can be obtained from a perturbative series expansion.

Quantum field theory (QFT) at finite temperature: Equilibrium properties

2021 ◽  
pp. 786-830
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Transitions ◽  
High Temperature ◽  
Dimensional Reduction ◽  
Finite Temperature ◽  
Finite Size ◽  
Quantum Field ◽  
Statistical Field ◽  
Statistical Field Theory

Some equilibrium properties in statistical quantum field theory (QFT), that is, relativistic QFT at finite temperature are reviewed. Study of QFT at finite temperature is motivated by cosmological problems, high energy heavy ion collisions, and speculations about possible phase transitions, also searched for in numerical simulations. In particular, the situation of finite temperature phase transitions, or the limit of high temperature (an ultra-relativistic limit where the temperature is much larger than the physical masses of particles) are discussed. The concept of dimensional reduction emerges, in many cases, statistical properties of finite-temperature QFT in (1, d − 1) dimensions can be described by an effective classical statistical field theory in (d − 1) dimensions. Dimensional reduction generalizes a property already observed in the non-relativistic example of the Bose gas, and indicates that quantum effects are less important at high temperature. The corresponding technical tools are a mode-expansion of fields in the Euclidean time variable, singling out the zero modes of boson fields, followed by a local expansion of the resulting (d − 1)-dimensional effective field theory (EFT). Additional physical intuition about QFT at finite temperature in (1, d−1) dimensions can be gained by considering it as a classical statistical field theory in d dimensions, with finite size in one dimension. This identification makes an analysis of finite temperature QFT in terms of the renormalization group (RG), and the theory of finite-size effects of the classical theory, possible. These ideas are illustrated with several simple examples, the φ4 field theory, the non-linear σ-model, the Gross–Neveu model and some gauge theories.

scholarly journals Energy levels of one-dimensional anharmonic oscillator via neural networks

2019 ◽  
Vol 34 (12) ◽  
pp. 1950088 ◽  
Author(s):  
Halil Mutuk
Keyword(s):  
Neural Network ◽  
Field Theory ◽  
Anharmonic Oscillator ◽  
Energy Levels ◽  
High Accuracy ◽  
Network System ◽  
Quantum Field ◽  
One Dimensional ◽  
Neural Network System ◽  
Good Agreement

In this work, we obtained energy levels of one-dimensional quartic anharmonic oscillator by using neural network system. Quartic anharmonic oscillator is a very important tool in quantum mechanics and also in the quantum field theory. Our results are in good agreement in high accuracy with the reference studies.

scholarly journals Self-similar extrapolation of nonlinear problems from small-variable to large-variable limit

2020 ◽  
Vol 34 (21) ◽  
pp. 2050208
Author(s):  
V. I. Yukalov ◽  
E. P. Yukalova
Keyword(s):  
Asymptotic Series ◽  
Nonlinear Problems ◽  
Numerical Convergence ◽  
Physical Problems ◽  
Variable Limit ◽  
Small Parameters ◽  
Self Similar ◽  
Similar Approximation ◽  
Similar Factor ◽  
Class Of Functions

Complicated physical problems are usually solved by resorting to perturbation theory leading to solutions in the form of asymptotic series in powers of small parameters. However, finite, and even large values of the parameters, are often of main physical interest. A method is described for predicting the large-variable behavior of solutions to nonlinear problems from the knowledge of only their small-variable expansions. The method is based on self-similar approximation theory resulting in self-similar factor approximants. The latter can well approximate a large class of functions, rational, irrational, and transcendental. The method is illustrated by several examples from statistical and condensed matter physics, where the self-similar predictions can be compared with the available large-variable behavior. It is shown that the method allows for finding the behavior of solutions at large variables when knowing just a few terms of small-variable expansions. Numerical convergence of approximants is demonstrated.

scholarly journals Exact four-point function and OPE for an interacting quantum field theory with space/time anisotropic scale invariance

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Hidehiko Shimada ◽  
Hirohiko Shimada
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scale Invariance ◽  
Asymptotic Series ◽  
Space Time ◽  
Quantum Field ◽  
Coupling Constant ◽  
Point Function ◽  
Calogero Model ◽  
Primary Operator

Abstract We identify a nontrivial yet tractable quantum field theory model with space/time anisotropic scale invariance, for which one can exactly compute certain four-point correlation functions and their decompositions via the operator-product expansion(OPE). The model is the Calogero model, non-relativistic particles interacting with a pair potential $$ \frac{g}{{\left|x-y\right|}^2} $$ g x − y 2 in one dimension, considered as a quantum field theory in one space and one time dimension via the second quantisation. This model has the anisotropic scale symmetry with the anisotropy exponent z = 2. The symmetry is also enhanced to the Schrödinger symmetry. The model has one coupling constant g and thus provides an example of a fixed line in the renormalisation group flow of anisotropic theories.We exactly compute a nontrivial four-point function of the fundamental fields of the theory. We decompose the four-point function via OPE in two different ways, thereby explicitly verifying the associativity of OPE for the first time for an interacting quantum field theory with anisotropic scale invariance. From the decompositions, one can read off the OPE coefficients and the scaling dimensions of the operators appearing in the intermediate channels. One of the decompositions is given by a convergent series, and only one primary operator and its descendants appear in the OPE. The scaling dimension of the primary operator we computed depends on the coupling constant. The dimension correctly reproduces the value expected from the well-known spectrum of the Calogero model combined with the so-called state-operator map which is valid for theories with the Schrödinger symmetry. The other decomposition is given by an asymptotic series. The asymptotic series comes with exponentially small correction terms, which also have a natural interpretation in terms of OPE.

scholarly journals Symmetries and Metamorphoses

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 907
Author(s):  
Giuseppe Vitiello
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Arrow Of Time ◽  
Quantum Field ◽  
Continuous Symmetry ◽  
Spontaneous Breakdown ◽  
Symmetry Properties ◽  
Fractal Patterns ◽  
Symmetry Transformations ◽  
Self Similar

In quantum field theory with spontaneous breakdown of symmetry, the invariance of the dynamics under continuous symmetry transformations manifests itself in observable ordered patterns with different symmetry properties. Such a dynamical rearrangement of symmetry describes, in well definite formal terms, metamorphosis processes. The coherence of the correlations generating order and self-similar fractal patterns plays a crucial role. The metamorphosis phenomenon is generated by the loss of infrared contributions in physical states and observables due to their localized nature. The dissipative dynamics and evolution, the arising of the arrow of time and entanglement are also discussed. The conclusions may be extended to biology and neuroscience and to some aspects of linguistics in the transition from syntax to semantics (generation of meanings).

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